UN Secretary General Ban Ki-moon Monday urged Israel and the Islamist Hamas movement to renew a humanitarian ceasefire in Gaza even as Israel announced that it has embarked on an "unlimited ceasefire" policy in the coastal enclave after 21 days of conflict claimed over 1,030 Palestinian lives.

In his appeal, Ban called on those responsible to "step back from provoking or inflicting yet more tragic violence on civilians there", Xinhua reported.

"The secretary general calls on the parties to renew a humanitarian pause in Gaza and reiterates his demand for a durable ceasefire that could set the ground for the start of comprehensive negotiations," said a statement issued here by Ban's spokesman.

"Following a largely observed 12-hour humanitarian pause July 26, the secretary general called on all parties to prolong the suspension of the fighting for an additional extendable period of 24 hours to allow vital humanitarian efforts to continue, including relief operations," the statement said.

"The parties have expressed serious interest in this request but have not yet agreed on the timing of its implementation," it said.

A Palestinian was killed and 10 others were injured Sunday after Israeli war jets resumed air strikes on Gaza, where a UN-proposed humanitarian ceasefire for 42 hours between Israel and Hamas collapsed.

On Sunday afternoon, Hamas spokesman Sami Abu Zuhri said in an emailed press statement that Hamas and the Palestinian factions agreed to accept the UN-proposed ceasefire for 24 hours, but Israel rejected it.

Ban's statement came just hours after the UN Security Council adopted a presidential statement in the early hours of Monday to voice its "grave concern" about the situation in the Middle East, and issue an urgent appeal to Israel and Hamas for an immediate humanitarian ceasefire in Gaza, where more than 1,000 people on both sides were killed over the past weeks.

"The Security Council expresses strong support for the call by the international partners and the secretary-general of the United Nations for an immediate and unconditional humanitarian ceasefire, allowing for the delivery of urgently needed assistance, and they urged all parties to accept and fully implement the humanitarian ceasefire into the Eid period and beyond," the 15-nation council said in the statement.

Representatives of Palestine and Israel to the UN, however, voiced disappointment at the Security Council statement endorsing a humanitarian ceasefire in Gaza.

Riyad Mansour, the Palestinian permanent observer to the UN, was the first to speak of disappointment.

"We were expecting to see the Security Council deal with the issue of providing protection for our people and to deal with legitimate concerns of our people in the Gaza Strip," Mansour said.

For his part, Ambassador Ron Prosor of Israel was also disappointed that there was no mention of Hamas, which rules over Gaza.

"We heard a presidential statement right now from the Security Council that miraculously managed not to mention Hamas or rockets or Israel's right to defend its citizens," he said.

In his statement Monday, the secretary-general said he welcomed the Security Council's strong support for his call for a humanitarian ceasefire.

"As people around the world mark Eid ul-Fitr, the end of the holy month of Ramadan and a time for overcoming differences, the secretary-general calls on parties to build on the current calm," said Ban's statement.

Meanwhile, Israel said Monday morning that it has embarked on an "unlimited ceasefire" policy in Gaza.

The new policy, adopted amid mounting international pressure to halt hostilities, means the Israeli military will halt the deliberate attacks in Gaza and will open fire only in retaliation to Gaza militant fire, an Israeli official told Xinhua.

"We are now on 'unlimited ceasefire', as decided by the political echelon," the source said. The Prime Minister's Office was not immediately available for comment.

However, according to local media reports, although the military seems to be holding fire on the ground and from the air, it will continue to destroy Hamas's cross-border tunnels.

Rocket fire from Gaza also declined sharply Monday, with only a single incident in which a rocket was fired Monday morning at the city of Ashkelon on Israel's southern coast hitting an open field.

An Israeli military spokesperson said that following the incident, "the Israel Defence Forces retaliated towards Beit Lahyia area from which the rocket was fired".

The new ceasefire policy comes a day after US President Barack Obama spoke on the phone with Israeli Prime Minister Benjamin Netanyahu, demanding "an immediate, unconditional humanitarian ceasefire that ends hostilities now and leads to a permanent cessation of hostilities based on the November 2012 ceasefire agreement" brokered by Egypt.